Use the parabola tool to graph the quadratic function f(x)=−x2+4. Graph the parabola by first plotting its vertex and then plotting a second point on the parabola.
Answer:
see below
Step-by-step explanation:
f(x) = -x^2 +4
The vertex form is
y = a(x-h)^2 +k
Rewriting
f(x) = -(x-0)^2 +4
The vertex is (0,4) and a = -1
Since a is negative we know the parabola opens downward
f(x) = -(x^2 -4)
We can find the zeros
0 = -(x^2 -2^2)
This is the difference of squares
0 = -(x-2)(x+2)
Using the zero product property
x-2 =0 x+2 =0
x=2 x=-2
(2,0) (-2,0) are the zeros of the parabola and 2 other points on the parabola
We have the maximum ( vertex) and the zeros and know that it opens downward, we can graph the parabola
Answer:
Your vertex is (4,0)
Step-by-step explanation:
Find the length of the segment indicated. Round your answer to the nearest 10th if necessary.
Answer:
x=13.6
Step-by-step explanation:
By Pythagoras theorem, 5.5^2+x^2=14.7^2. x^2=14.7^2-5.5^2. x=13.6
cos theta / sec theta -1 - sin theta / 1+cos theta = 2 cot theta
Step-by-step explanation:
Explanation is in the attachmentHope it is helpful to you
Correct and fastest answer gets brainest! 12 divided 2/5
30
Answer:
12÷2/5=12*5/2=30 is a required answer
Answer:
30
Step-by-step explanation:
what is the cosine of 122.2
cosine 122.2 = -0.532876276......
Three red balls, 5 green balls and a number of blue balls are put together in a sac. One ball is picked at random from the sac. If the probability of picking a red ball is 1|6, find the a) The number of blue balls in sac. B) the probability of picking a green ball
Answer:
total balls = 18 .... 3/x = 1/6
blue = 10 ... 18-(5+3) = 10
p of green = 5/18 = .277
Step-by-step explanation:
Grandma is making a quilt. She has 540 cm of fabric to border the quilt. What is the greatest possible area for the quilt?
Question 1 options:
11 664 cm^2
18225 cm^2
72900 cm^2
291600 cm^2
Show your work:
Answer:
18225 cm²
Step-by-step explanation:
Divide 540 by 4 to get the length of all sides
540/4 = 135
Square 135 to get the max possible size
135² = 18225
18225 cm² is the greatest possible area for the quilt.
What is area?The measurement that expresses the size of a region on a plane or curved surface is called area. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a form or planar lamina.
Given
Divide 540 by 4 to obtain the length of all sides
540/4 = 135
Square 135 to acquire the max possible size
135² = 18225
18225 cm² is the greatest possible area for the quilt.
To learn more about area refer to:
https://brainly.com/question/25292087
#SPJ2
need some help with this
Answer:
y=4x-7
Step-by-step explanation:
here,
the equation of straight line in slope intercept form is;
y=mx+c
( m= slope
c= y-intercept )
soo..
the question has asked for slope 4 i.e. m=4
and y- intercept -7 i.e. c= -7
now.
the required equation is
y= 4x-7
mark me brainliest and follow me ... please
2/5(1/3x-15/8)-1/3(1/2-2/3x)
Answer:
[tex]\frac{16}{45}x-\frac{11}{12}[/tex]
Step-by-step explanation:
We are given that an expression
[tex]\frac{2}{5}(1/3x-15/8)-\frac{1}{3}(1/2-2/3x)[/tex]
We have to find the equivalent expression.
[tex]\frac{2}{5}(\frac{1}{3}x-\frac{15}{8})-\frac{1}{3}(\frac{1}{2}-\frac{2}{3}x)[/tex]
[tex]\frac{2}{5}\times \frac{1}{3}x-\frac{2}{5}\times \frac{15}{8}-\frac{1}{3}\times \frac{1}{2}-\frac{1}{3}\times (-\frac{2}{3}x)[/tex]
Using the the property
[tex]a\cdot (c-b)=a\cdot c-a\cdot b[/tex]
[tex]\frac{2}{5}(1/3x-15/8)-\frac{1}{3}(1/2-2/3x)[/tex]
[tex]=\frac{2}{15}x-\frac{3}{4}-\frac{1}{6}+\frac{2}{9}x[/tex]
[tex]=\frac{6x+10x}{45}+\frac{-9-2}{12}[/tex]
[tex]=\frac{16}{45}x-\frac{11}{12}[/tex]
[tex]\frac{2}{5}(1/3x-15/8)-\frac{1}{3}(1/2-2/3x)=\frac{16}{45}x-\frac{11}{12}[/tex]
Which table of values could be generated by the equation 10x+5y=15? (Will give brainlest and 21 points)
Answer:
(For the image) A
Step-by-step explanation:
what is 3x10x178 I need help asap
Answer:
3x10=30 30x178=5,430
Step-by-step explanation:
[tex]3 \times 10 \times 178 \\ 30 \times 178 \\ 5340 \: \: answer[/tex]
If f is continuous for all x, which of the following integrals necessarily have the same value?
Answer:
B
Step-by-step explanation:
Given the three integrals, we want to determine which integrals necessarily have the same value.
We can let the first integral be itself.
For the second integral, we can perform a u-substitution. Let u = x + a. Then:
[tex]\displaystyle du = dx[/tex]
Changing our limits of integration:
[tex]u_1=(0)+a=a \text{ and } u_2 = (b+a)+a = b+2a[/tex]
Thus, the second integral becomes:
[tex]\displaystyle \int_{0}^{b+a}f(x+a)\, dx = \int_a^{b+2a} f(u)\, du[/tex]
For the third integral, we can also perform a u-substitution. Let u = x + c. Then:
[tex]\displaystyle du = dx[/tex]
And changing our limits of integration:
[tex]\displaystyle u_1=(a-c)+c=a \text{ and } u_2=(b-c)+c=b[/tex]
Thus, our third integral becomes:
[tex]\displaystyle \int_{a-c}^{b-c}f(x+c)\, dx = \int_{a}^{b} f(u)\, du[/tex]
Since the only difference between f(x) and f(u) is the variable and both the first and third integral have the same limits of integration, our answer is B.
Can someone help me with this math homework please!
Answer:
Second optionAs the x-values go to negative infinity, the function´s values go to positive. infinity.
--------------------------
Hope it helps...
have a great day!!
Answer:
(B) As the x-values go to negative infinity, the function's values go to positive infinity.
Step-by-step explanation:
The x-values the answer choices are talking about are the values on the x-axis.
Looking at the graph, when the x-values go to negative infinity (meaning it keeps on going left, or negative), the function goes up, meaning the function goes to positive infinity.
When the x-values go to positive infinity (meaning it keeps on going right, or positive), the function goes up, meaning the function goes to positive infinity.
Out of all the answer choices, only B agrees with the observations written above.
Hope that helps (●'◡'●)
What is the range of f(x)=4^x
Answer:
B
Step-by-step explanation:
At - infinity, the function will tend to 0 and at +infinity, the function will tend to +infinity. Those are the two extremas of the function and extremas define the range. Range is all positive real number
A house on the market was valued at $472,000. After several years, the value increased by 19%. By how much did the house's value increase in dollars? What is the current value of the house?
Step-by-step explanation:
Increase in dollars
19/100 x 472.000 = $89,670
and the current value house is $472,000 + $89,670 = $561,680
If the speed of an object in motion is doubled, its kinetic energy becomes how many times the original kinetic energy
Answer: Becomes four times
Step-by-step explanation:
Given
Speed is doubled for a moving object
Suppose initial speed is u
Increased speed is 2u
Kinetic Energy is given by
[tex]\Rightarrow K=0.5mu^2[/tex]
When speed is doubled
[tex]\Rightarrow K'=0.5m(2u)^2\\\Rightarrow K'=(0.5mu^2)\times 4\\\Rightarrow K'=4K[/tex]
Kinetic energy becomes four times
Find the length of side BC give your answer to three significant figures
Answer:
19.4 cm
Step-by-step explanation:
Hi there!
This is a right triangle. We're given an angle, the side adjacent to the angle and we're solving for the hypotenuse. Given this information, we can use the cosine ratio:
[tex]cos\theta=\frac{adj}{hyp}[/tex]
Plug in the given angle and side
[tex]cos71=\frac{6.3}{BC}\\BC=\frac{6.3}{cos71} \\BC=19.4[/tex]
Therefore, the length of BC is 19.4 cm when rounded to 3 significant figures.
I hope this helps!
Do not round your answer. Type in the number with the decimal. 15% of 25 is
Answer:
to add on to what the other dude said its 4
Step-by-step explanation:
State what additional information is required in order to know that the triangle in the image below are congruent for the reason given…
Reason: HL Postulate
Answer:
FG ≈ FL (Both are hypotenuse, supposed to be equal in order to the congruency to become HL)
Answered by GAUTHMATH
A car travels 600 km in 6 hours. at what rate of speed is the car traveling?
Step-by-step explanation:
100Km/hours......V/T
When AG = 16 ft, find the area of the region that is NOT shaded. Round to the nearest tenth.
Answer:
730.88
Step-by-step explanation:
Area of the entire circle = pi * r^2
r = 16
Area = 3.14 * 16^2
Area = 803.84
1/4 of the circle contains the shaded area. It's area = 1/4 * 803.84
Area of 1/4 circle =
200.96
the area of the triangle
Area = 1/2 AG * G?
AG and G? are equal
Area = 1/2 * 16^2
Area = 128
Area of 1/4 circle - area of the triangle = area of the shaded portion
shaded portion = 200.95 - 128
Shaded Portion = 72.96
So the area of the unshaded part
unshaded = 803.84 - 72.96
Unshaded = 730.88
Convert to decimal degrees.
-(167° 31”)
[?]°
Enter your answer with three decimal places.
Answer:
The angle in decimal form is 167.009°.
Step-by-step explanation:
We know an angle in terms of integer angles, minutes and seconds, whose conversion into decimal degrees is expressed by the following formula:
[tex]\theta = n + \frac{m}{60}+\frac{s}{3600}[/tex] (1)
Donde:
[tex]n[/tex] - Integer angle, in sexagesimal degrees.
[tex]m[/tex] - Minutes.
[tex]s[/tex] - Seconds.
If we know that [tex]n = 167[/tex], [tex]m = 0[/tex] and [tex]s = 31''[/tex], then the angle in decimal form is:
[tex]\theta = 167^{\circ}+\frac{0}{60}^{\circ} + \frac{31}{3600}^{\circ}[/tex]
[tex]\theta = 167.009^{\circ}[/tex]
The angle in decimal form is 167.009°.
Given: x - 7 > -2.
Choose the solution set.
A. {x | x R, x > 14}
B. {x | x R, x > -5}
C. {x | x R, x > 5}
D. {x | x R, x > -9}
Given set:- x - 7 > - 2
Solving It:-
x - 7 > - 2
x > -2 + 7 [Here '7' is greater than '-2' So Sign Changes To Positive]
x > 5
So Correct Solution Set Will Be
Option C= {x | x R, x > 5}
Hope This Helps YouAisha wants to paint the four walls of her living room.
Each wall is 2.2 m high and 5.5 m long.
One wall has a door of 1.8 m by 0.9 m.
Tins of paint cost £13 per 2 L tin.
Each litre of paint can cover 8 m2 of wall.
There is an offer of: Buy 2 tins get the 3rd at half price.
How much will Aisha pay to paint her living room?
Answer:
£32.50
Step-by-step explanation:
my first question to the teacher : so, no windows in the living room ?
so, it is a square living room with 5.5 m side length.
but each wall is a rectangle of 2.2 × 5.5 m.
for one wall we have to deduct a door area of 1.8×0.9 m.
so, one wall
2.2 × 5.5 = 12.1 m²
4 walls
4 × 12.1 = 48.4 m²
minus one door area
1.8 × 0.9 = 1.62 m²
48.4 - 1.62 = 46.78 m² total paint area
1 L paint covers 8 m².
so, we need 46.78/8 = 5.85 liters.
she gets the paint in 2 L tins. so, she needs 3 tins (6 L).
each tin costs £13.
and because she buys 3 tins, she gets the third one for half the price (13/2 = £6.50).
so, she has to pay
2×13 + 6.50 = 26 + 6.50 = £32.50
Can someone help me with this math homework please!
Answer:
f(n+1) = f(n) - 5
Step-by-step explanation:
Just find some relationship between 2 numbers that are next to each other.
the tens digit of a two digit number is 5 greater the units digit. If you subtract double the reversed number from it, the result is a fourth of the original number. Find the original number.
Given:
The tens digit of a two digit number is 5 greater the units digit.
If you subtract double the reversed number from it, the result is a fourth of the original number.
To find:
The original number.
Solution:
Let n be the two digit number and x be the unit digit. Then tens digit is (x+5) and the original number is:
[tex]n=(x+5)\times 10+x\times 1[/tex]
[tex]n=10x+50+x[/tex]
[tex]n=11x+50[/tex]
Reversed number is:
[tex]x\times 10+(x+5)\times 1=10x+x+5[/tex]
[tex]x\times 10+(x+5)\times 1=11x+5[/tex]
If you subtract double the reversed number from it, the result is a fourth of the original number.
[tex]11x+50-2(11x+5)=\dfrac{1}{4}(11x+50)[/tex]
[tex]11x+50-22x-10=\dfrac{1}{4}(11x+50)[/tex]
[tex]40-11x=\dfrac{1}{4}(11x+50)[/tex]
Multiply both sides by 4.
[tex]160-44x=11x+50[/tex]
[tex]160-50=11x+44x[/tex]
[tex]110=55x[/tex]
Divide both sides by 55.
[tex]\dfrac{110}{55}=x[/tex]
[tex]2=x[/tex]
The unit digit is 2. So, the tens digit is [tex]2+5=7[/tex].
Therefore, the original number is 72.
Find cosθ+cos3θ+cos5θ+cos7θ by using the Sum-to-Product Formula.
Please also show your work as well. Thanks!
Answer:
[tex] \rm\displaystyle 4\cos( \theta) \cos \left( {2\theta} \right) \cos \left( {4 \theta } \right) [/tex]
Step-by-step explanation:
I assume the question want us to rewrite cosθ+cos3θ+cos5θ+cos7θ by using Sum-to-Product Formula and note that it's not an equation therefore θ can never be specified
===========================
so we want to rewrite cosθ+cos3θ+cos5θ+cos7θ by using Sum-to-Product Formula the good news is that the number of the function of the given expression is even so there's a way to do so, rewrite the expression in parentheses notation:
[tex] \rm\displaystyle \left( \cos( \theta) + \cos(3 \theta) \right) + \left(\cos(5 \theta) + \cos(7 \theta) \right)[/tex]
recall that,Sum-to-Product Formula of cos function:
[tex] \rm \boxed{\displaystyle \cos( \alpha ) + \cos( \beta ) = 2 \cos \left( \frac{ \alpha + \beta }{2} \right) \cos \left( \frac{ \alpha - \beta }{2} \right) }[/tex]
notice that we have two pair of function with which we can apply the formula thus do so,
[tex] \rm\displaystyle \left( 2\cos \left( \frac{ \theta + 3 \theta}{2} \right)\cos \left( \frac{ \theta - 3 \theta}{2} \right) \right) + \left(2\cos \left( \frac{5 \theta + 7 \theta}{2} \right) \cos \left( \frac{5 \theta - 7 \theta}{2} \right) \right)[/tex]
simplify addition:
[tex] \rm\displaystyle \left( 2\cos \left( \frac{4 \theta}{2} \right)\cos \left( \frac{ - 2\theta }{2} \right) \right) + \left(2\cos \left( \frac{12 \theta }{2} \right) \cos \left( \frac{ - 2 \theta}{2} \right) \right)[/tex]
simplify division:
[tex] \rm\displaystyle \left( 2\cos \left( {2 \theta} \right)\cos \left( { - \theta } \right) \right) + \left(2\cos \left( {6 \theta } \right) \cos \left( { - \theta} \right) \right)[/tex]
By Opposite Angle Identities we acquire:
[tex] \rm\displaystyle \left( 2\cos \left( {2 \theta} \right)\cos \left( { \theta } \right) \right) + \left(2\cos \left( {6 \theta } \right) \cos \left( { \theta} \right) \right)[/tex]
factor out 2cosθ:
[tex] \rm\displaystyle 2 \cos( \theta) (\cos \left( {2 \theta} \right) + \cos \left( {6 \theta } \right) )[/tex]
once again apply Sum-to-Product Formula which yields:
[tex] \rm\displaystyle 2 \cos( \theta) (2\cos \left( {4\theta} \right) \cos \left( {2 \theta } \right) )[/tex]
distribute:
[tex] \rm\displaystyle 4\cos( \theta) \cos \left( {2\theta} \right) \cos \left( {4 \theta } \right) [/tex]
and we're done!
use a double angle or half angle identity to find the exact value of each expression
Answer:
Step-by-step explanation:
There are 2 very distinct and important things that we need to know before completing the problem. First is that we are given that the cos of an angle is 1/3 (adjacent/hypotenuse) and it is in the first quadrant. We also need to know that the identity for sin2θ = 2sinθcosθ.
We already know cos θ = 1/3, so we need now find the sin θ. The sin ratio is the side opposite the angle over the hypotenuse, and the side we are missing is the side opposite the angle (we do not need to know the angle; it's irrelevant). Set up a right triangle in the first quadrant and label the base with a 1 (because the base is the side adjacent to the angle), and the hypotenuse with a 3. Find the third side using Pythagorean's Theorem:
[tex]3^2=1^2+y^2[/tex] which simplifies to
[tex]9=1+y^2[/tex] and
[tex]y^2=8[/tex] so
[tex]y=\sqrt{8}=2\sqrt{2}[/tex] so that's the missing side. Now we can easily determine that
[tex]sin\theta=\frac{2\sqrt{2} }{3}[/tex]
Now we have everything we need to fill in the identity for sin2θ:
[tex]2sin\theta cos\theta=2(\frac{2\sqrt{2} }{3})(\frac{1}{3})[/tex] and multiply all of that together to get
[tex]2sin\theta cos\theta=\frac{4\sqrt{2} }{9}[/tex]
Find f(-3) for f(x) = 4(2)^x
O A. -32
O B. 1/2
O C. -24
O D. 1/8
Answer:
B. 1/2
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Functions
Function NotationStep-by-step explanation:
Step 1: Define
Identify
f(x) = 4(2)ˣ
Step 2: Evaluate
Substitute in x [Function f(x)]: f(-3) = 4(2)⁻³Exponents: f(-3) = 4(1/8)Multiply: f(-3) = 1/2Find cos 0
A. 15/8
B. 15/17
C. 8/15
D. 8/17
Answer:
A.15/8
Step-by-step explanation:
the answer is 15/8
Answer:
D.
[tex]{ \tt{ \cos( \theta) = \frac{adjacent}{hypotenuse} }} \\ \\ { \tt{ \cos( \theta) = \frac{8}{ \sqrt{ {15}^{2} + {8}^{2} } } }} \\ \\ { \tt{ \cos( \theta) = \frac{8}{ \sqrt{289} } }} \\ \\ { \tt{ \cos( \theta) = \frac{8}{17} }}[/tex]